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AN ISOLATED GENIUS IS GIVEN HIS DUE

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IN some ways, mathematicians are finally beginning to penetrate the mind of Srinivasa Ramanujan.

One hundred years have passed since Ramanujan was born in the small city of Kumbakonam in southern India. When he died 32 years later, he left a strange, raw legacy, about 4,000 formulas written on the pages of three notebooks and some scrap paper.

Some of the power and originality of Ramanujan's mathematics was understood a few years before his death. His contemporaries saw from the theorems scrawled across his pages that he possessed a genius for calculating the hidden laws and relationships that govern the wilderness of numbers.

But Ramanujan was uneducated in standard mathematics and isolated by geography for most of his productive life. Often his formulas seemed as obscure as they were elegant. He worked in a place of his own and a way of his own, drawing his formulas and theorems from a mental landscape that remained far from the frontier of mathematics as it was seen in his day.

Now his work is flowing into mathematics and science more deeply than could have been imagined a generation ago. Computers, with special programs to manipulate algebraic quantities, have made it possible for more ordinary mathematicians to pick up the trail of his thought. And modern physics, from the superstring theory of cosmology to the statistical mechanics of complicated molecular systems, finds itself turning more and more often to the pure findings of number theory and complex analysis - the worlds of Ramanujan.

So researchers are intensifying a process of forensic mathematics, or mathematical archeology - poring over the rough pages, trying to understand the formulas and prove them. As they learn more of why Ramanujan chose particular paths, they sense a foundation that has not yet been revealed.

''When he pulled extraordinary objects out of the air, they weren't just curiosities but they were the right things,'' said Jonathan M. Borwein of Dalhousie University in Halifax, Nova Scotia, one of many mathematicians who has lately found himself turning to Ramanujan's formulas. ''They are elusive evidence of a theory that's lurking around somewhere that he never made explicit.''

The trail is hard to follow. Out of necessity and then perhaps out of habit, Ramanujan worked in a style that awes and frustrates modern mathematicians. He used a slate, jotting down formulas, erasing them with his elbow, jotting down more, and then recording a result in his precious notebook only when it had reached final form.

The intermediate results, the links of the chain, are lost. Unlike mainstream mathematicians, he felt no need to prove that a result was true. His legacy is simply a set of discoveries. 'A Feel for Things'

''He seems to have functioned in a way unlike anybody else we know of,'' Dr. Borwein said. ''He had such a feel for things that they just flowed out of his brain. Perhaps he didn't see them in any way that's translatable. It's like watching somebody at a feast you haven't been invited to.''

So mathematicians have spent years - often valuable and productive years - proving theorems that Ramanujan knew to be true. Deriving the formulas has often been more illuminating than the formulas themselves. Whole new subdisciplines within mathematics have blossomed around ideas that Ramanujan put forward in a peculiar, stark isolation.

With the special excuse of his centennial year, mathematicians are gathering to discuss the implications of Ramanujan's work at meetings in the United States and India. They have far more raw material to work with than ever before, because the last decade has brought a new effort to find and organize the pages that make up his legacy.

A University of Illinois mathematician, Bruce Berndt, has spent years editing the notebooks, tracking down sources and relationships and, above all, proving as many of the unproved theorems as possible. A mathematician at Pennsylvania State University, George Andrews, has been performing the same task with the so-called Lost Notebook, 130 pages of scrap paper from the last year of Ramanujan's life.

''The work of that one year, while he was dying, was the equivalent of a lifetime of work for a very great mathematician,'' said Richard Askey of the University of Wisconsin, who has collaborated with Dr. Andrews in trying to understand some of Ramanujan's work.

''What he accomplished was unbelievable,'' Dr. Askey said. ''If it were in a novel, nobody would believe it.''

Ramanujan might have died in complete obscurity if he had not written a series of desperate, bold letters to English mathematicians in 1912 and 1913. By then he was 25 years old, working as a $:30-a-year clerk after several years of unemployment, unwilling to put aside his slate and formulas.

His family was Hindu, high-caste but poor. His father and grandfather before him worked as clerks for cloth merchants. Ramanujan was lucky enough to have a fairly good high school education in Kumbakonam, and he began his creative exploration of mathematics after discovering the few outdated and second-rank textbooks in the library there. 'An Unknown Hindu Clerk'

His intellect stood out clearly, but in college at Madras, about 150 miles north of his birthplace, he failed again and again to pass examinations in other subjects. In mathematics itself, he had no teacher. He worked, as the English mathematician Godfrey J. Hardy later said, ''in practically complete ignorance of modern European mathematics.''

Hardy was not the first mathematician to receive a letter from this ''unknown Hindu clerk,'' as he recalled -''at the best, a half-educated Indian.'' But he was the first to understand what the letter contained.

Ramanujan's letters said, in effect, I know the following . . . and I also know this . . . and, by the way, I have discovered this. He offered a carefully chosen selection of his theorems. Most were in the form of identities -statements that some familiar quantity, like pi, was equal to some unfamiliar quantity, or that two unfamiliar quantities were equal.

Hardy examined them with bewilderment. A few struck chords of recognition, he said later; he thought he had proved similar statements himself. Some he thought he could prove if he tried - and he succeeded, although with surprising difficulty.

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''I had never seen anything in the least like them before,'' he said. ''A single look at them is enough to show that they could only be written down by a mathematician of the highest class. They must be true because, if they were not true, no one would have had the imagination to invent them.''

Furthermore, Hardy could tell that Ramanujan was holding some things back, offering specific examples of theorems for which he surely must have discovered more general versions. He arranged an invitation to Cambridge University, and in 1913 Ramanujan arrived, leaving his wife behind. He stayed for nearly six years.

The two men collaborated often. Hardy remembered a slight man, of medium height, with eyes through which some light seemed to shine. Ramanujan remained a strict vegetarian, cooking all his own food in his rooms, and when he fell mysteriously ill in 1917, Hardy thought his vegetarianism contributed to his failing health. Shared Fascination

Years later, Hardy took some pains to dispel the idea, perhaps a byproduct of subtle English racism, that Ramanujan was some sort of Asian curiosity - either an ''inspired idiot'' or ''some mysterious manifestation of the immemorial wisdom of the East.'' On the contrary, in Hardy's eyes he was a deliberate rationalist, often shrewd, and not nearly so religious as his dietary habits made him appear.

They shared a fascination with numbers as almost living things, or characters in a story. They thought about round numbers, defined as numbers with only small factors, like 300, 2#2X3X5#2. They worked on the question of how common such numbers are, in strict mathematical terms, and on many problems more difficult to put into words. 'A Very Interesting Number'

One day after Ramanujan fell ill, Hardy visited him in a taxicab and remarked that the cab's number had been rather uninteresting - 1729, or 7X13X19. ''No, it is a very interesting number,'' Ramanujan responded, as Hardy later told the story. ''It is the smallest number expressible as a sum of two cubes in two different ways.'' (It is the sum of 1X1X1 and 12X12X12, and it is also the sum of 9X9X9 and 10X10X10.) Hardy understood and appreciated Ramanujan more than any of his contemporaries. But even he could not see beyond the blinkers of his time and place. To him, Ramanujan's story was ultimately a tragedy - of inadequate education and of genius unguided. When he finally came to assess the younger mathematician's work and its likely influence on the future of his subject, he expressed disappointment.

''It has not the simplicity and the inevitableness of the very greatest work,'' Hardy wrote in 1927. ''It would be greater if it were less strange.''

Few mathematicians accept that assessment today, as strangeness comes into the light and Hardy recedes into Ramanujan's greater shadow.

''Hardy thought it was a shame that Ramanujan wasn't born a hundred years earlier,'' Dr. Askey said. That was the great age of formulas, the era of ground-laying work by such mathematicians as Euler and Gauss. ''My comment is that it's a shame Ramanujan wasn't born a hundred years later,'' he said. ''We're trying to do problems in several variables now - the problems are harder, and it would be marvelous to have somebody with his intuition to help get started.''

Not that his intuition was infallible. Ramanujan made some errors, once claiming to have found a formula for the approximate number of primes less than any given number. No such formula exists. He was too optimistic, and it was the optimism of an earlier time; by the 19th century, mathematicians had learned that some problems could never be solved, but Ramanujan's isolation shielded him from their doubts as much as from their knowledge.

In 1919, increasingly ill, having entered and left a nursing home and several sanitariums, Ramanujan returned to India. He continued to work feverishly, fighting the pain of his mysterious ailment, writing on whatever paper he could find. The next April, at the age of 32, he died. Papers Discovered in 1976

The work of his last year, 130 unlabeled pages, came to rest at the library of Trinity College, Cambridge, where they lay in a box, along with assorted bills and letters, until Dr. Andrews of Pennsylvania State University found them in 1976. This was the Lost Notebook.

''It's a bizarre term to use for something that was in the major library of the major college in England,'' Dr. Borwein said, ''but in terms of people appreciating its contents, it was certainly true.''

Dr. Andrews found that Ramanujan had cleared a path that mathematicians had not succeeded in matching in the intervening half century. Many discoveries concerned a family of identities he called mock theta functions - ''simple assertions in arithmetic,'' as Dr. Andrews put it, although ''their implications are quite profound.'' Seeds of 'Ramanujan's Garden'

Such mathematics has helped drive one of the major new conceptions of theoretical physics, superstring theory, as the physicist Freeman Dyson told a Ramanujan conference last month. ''As pure mathematics, it is as beautiful as any of the other flowers that grew from seeds that ripened in Ramanujan's garden,'' he said.

Another identity was used last year to enable a computer to calculate millions of digits of pi. It converges on the exact value with far greater efficiency than any previous method. Yet, as always, Ramanujan had merely asserted his discovery; only later did Dr. Borwein and his brother, Peter B. Borwein, prove rigorously that those millions of digits really were pi.

The applications of Ramanujan's magical-seeming formulas make mathematicians think that he was mining a deep vein of theory, the full outlines of which are not yet known. But many prefer not to dwell on just how Ramanujan was able to think as he did.

Hardy looked at Ramanujan's origins and saw a crippling neglect by an inadequate educational system cut off from European society. Still, as mathematicians realize now, Ramanujan had a decent high school, a handful of books and the traditions of a culture that allowed him to aspire to a life as a scholar.

Those looking for lessons in his brief, rich life sometimes note that now, one century later, much of the planet lacks that much.

''Ramanujan is important not just as a mathematician but because of what he tells us that the human mind can do,'' Dr. Askey said. ''Someone with his ability is so rare and so precious that we can't afford to lose them. A genius can arise anywhere in the world.'' A Mysterious Formula for Pi Mathematicians find many of Ramanujan's formulas to be both beautiful and obscure. To their surprise, the formula above provides an extremely rapid way to calculate the value of pi, an age-old preoccupation. Only last year, a computer scientist used a version of Ramanujan's formula to calculate pi to 17 million places. Only after this success were mathematicians able to prove why Ramanujan's insight was correct.

Correction: July 23, 1987

Thursday, Late City Final Edition

His stay at Cambridge University lasted just under five years; the article said nearly six. And the mathematician Godfrey Hardy's middle initial was H.

A version of this article appears in print on July 14, 1987, on Page C00001 of the National edition with the headline: AN ISOLATED GENIUS IS GIVEN HIS DUE. Order Reprints|Today's Paper|Subscribe